A new basin-sampling scheme is introduced to obtain equilibrium thermodynamic properties by combining results from global optimisation and parallel tempering calculations. Regular minimisation is used to obtain a two-dimensional density of states. A model anharmonic form is optimised using a multihistogram approach for potential energy bins corresponding to local minima, connecting the results obtained for low and high temperatures. This procedure provides accurate densities of states and thermodynamic properties for benchmark atomic clusters exhibiting broken ergodicity. It can also be used to calculate the potential energy density of local minima for distinct permutation-inversion isomers and distinct structures. (C) 2013 Elsevier B. V. All rights reserved.